Linear Dynamical System
This page contains resources about Linear Dynamical Systems, Linear Systems Theory, Dynamic Linear Models, Linear State Space Models and State-Space Representation, including temporal (Time Series) and atemporal Sequential Data. Subfields and Concepts * Linear SSM ** Discrete-time LDS ** Continuous-time LDS ** Linear Time-Invariant (LTI) system ** Linear Time-Variant System * Parametric models / Time Series models ** Autoregressive (AR) model / All-Pole model ** Moving Average (MA) model / All-Zero model ** ARMA model / Pole-Zero model ** Autoregressive Conditional Heteroskedasticity (ARCH) model ** Generalized ARCH (GARCH) model ** Vector Autoregressive (VAR) model ** Martin Distance (for comparing ARMA processes) * Kalman filter / Linear Gaussian SSM * Stochastic LDS * Structured LDS * Bayesian SSM ** Bayesian Time Series ** Bayesian LDS * SSM with Regime Switching / Jump Markov Linear Systems / Switching LDS / Switching SSM * Kernels on Dynamical Systems * Computer Vision ** Linear Dynamic Texture ** Kernel Dynamic Texture Online Courses Video Lectures * Introduction to Linear Dynamical Systems by Stephen Boyd * Topics in Mathematics with Applications in Finance by Peter Kempthorne, Choongbum Lee, Vasily Strela and Jake Xia Lecture Notes * Dynamic Systems and Control by Emilio Frazzoli & Munther Dahleh * Linear Systems Theory by John Lygeros and Federico A. Ramponi * Linear System Theory by Claire Tomlin * Time Series Econometrics by Peter C. B. Phillips * Time Series Econometrics by Eric Zivot * Econometrics II by Rauli Susmel * Applied Econometrics by Baum * Dynamical Systems and Stochastic Processes by Pierre Collet * Linear Dynamical Systems by Stephen Boyd * Applied Time Series Analysis * Time Series Analysis I by Suhasini Subba Rao * Applied Forecasting for Business and Economics by Rob J Hyndman * Lecture 10: Sequential Data Models by Geoffrey Hinton Books and Book Chapters See also Further Reading. * Brockett, R. W. (2015). Finite dimensional linear systems. SIAM. * Hyndman, R. J., & Athanasopoulos, G. (2013). Forecasting: principles and practice. OTexts. * Murphy, K. P. (2012). "Chapter 18: State space models". Machine Learning: A Probabilistic Perspective. MIT Press. * Barber, D. (2012). "Chapter 24: Continuous-State Markov Models". Bayesian Reasoning and Machine Learning. Cambridge University Press. * Barber, D. (2012). "Chapter 25: Switching Linear Dynamical Systems". Bayesian Reasoning and Machine Learning. Cambridge University Press. * Durbin, J., & Koopman, S. J. (2012). Time series analysis by state space methods. Oxford University Press. * Casti, J. L. (2012). Linear dynamical systems. Academic Press Professional. * Prado, R., & West, M. (2010). Time series: modeling, computation, and inference. CRC Press. * Tsay, R. S. (2010). Analysis of Financial Time Series. 3rd Ed. John Wiley & Sons. * Petris, G., Petrone, S., & Campagnoli, P. (2009). Dynamic Linear Models with R. Springer New York. * Hespanha, J. P. (2009). Linear systems theory. Princeton university press. * Zadeh, L. A., & Desoer, C. A. (2008). Linear System Theory: The State Space Approach''.'' Dover. * Antsaklis, P. J., & Michel, A. N. (2007). A Linear Systems Primer. Springer Science & Business Media. * Antsaklis, P. J., & Michel, A. N. (2006). Linear systems. Springer Science & Business Media. * Bishop, C. M. (2006). "Chapter 13: Sequential Data". Pattern Recognition and Machine Learning. Springer. * Gajic, Z. (2003). Linear dynamic systems and signals. Prentice Hall/Pearson Education. * Chatfield, C. (2003). The analysis of time series: an introduction. 6th Ed. CRC press. * Harrison, J., & West, M. (1999). Bayesian Forecasting & Dynamic Models. Springer. * Chen, C. T. (1998). Linear system theory and design. Oxford University Press. * Rugh, W. J. (1996). Linear system theory. Prentice Hall. * Hamilton, J. D. (1994). Time series analysis. Princeton University Press. * Callier, F. M., & Desoer, C. A. (1991). Linear System Theory. Springer New York. * Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter. Cambridge university press. * Harvey, A. C. (1993). Time series models. 2nd Ed. The MIT Press. * Delchamps, D. F. (1988). State space and input-output linear systems. Springer Science & Business Media. * Cryer, J. D. (1986). Time series analysis. Duxbury Press. * Kailath, T. (1980). Linear systems. Prentice-Hall. * Luenberger, D. G. (1979). Introduction to dynamic systems. John Wiley & Sons. Scholarly Articles * Archer, E., Park, I. M., Buesing, L., Cunningham, J., & Paninski, L. (2015). Black box variational inference for state space models. arXiv preprint arXiv:1511.07367. * Petris, G., & Petrone, S. (2011). State space models in R. Journal of Statistical Software, 41(4), 1-25. * Vishwanathan, S. V. N., Smola, A. J., & Vidal, R. (2007). Binet-Cauchy kernels on dynamical systems and its application to the analysis of dynamic scenes. International Journal of Computer Vision, 73(1), 95-119. * Chan, A. B., & Vasconcelos, N. (2007). Classifying video with kernel dynamic textures. In Computer Vision and Pattern Recognition, IEEE Conference on (pp. 1-6). IEEE. * Rudary, M., Singh, S., & Wingate, D. (2005). Predictive linear-Gaussian models of stochastic dynamical systems. Conference on Uncertainty in Artificial Intelligence. * Doretto, G., Chiuso, A., Wu, Y. N., & Soatto, S. (2003). Dynamic textures. International Journal of Computer Vision, 51(2), 91-109. * Martin, R. J. (2000). A metric for ARMA processes. IEEE transactions on Signal Processing, 48(4), 1164-1170. * Minka, T. (1999). From hidden markov models to linear dynamical systems. Technical Report, MIT. * Kim, C. J. (1994). Dynamic linear models with Markov-switching. Journal of Econometrics, 60(1-2), 1-22. * Ghahramani, Z., & Hinton, G. E. (1996). Parameter estimation for linear dynamical systems. Technical Report CRG-TR-96-2, University of Toronto, Dept. of Computer Science. * Kalman, R. E. (1963). Mathematical description of linear dynamical systems. Journal of the Society for Industrial and Applied Mathematics, Series A: Control, 1(2), 152-192. Software * Control Systems Toolbox - MATLAB * System Identification Toolbox - MATLAB * Econometrics Toolbox - MATLAB * Kalman filter and Linear Dynamical System -MATLAB * DLM Matlab Toolbox * Python Control Systems Toolbox * dynpy - Python * PyDSTool - Python * Statsmodels - Statistical Modeling and Econometrics in Python * PyFlux - Python * DLM - R * dynr - R * timeSeries - R * zoo - R See also * Stochastic Process * Monte Carlo Methods * Variational Methods * Hidden Markov Models * Estimation Theory / Statistical Signal Processing * Nonlinear Systems * Computational Finance Other Resources * State Space Models in Python * Time Series Analysis in R * Time Series - Notebook * State-Space Reconstruction - Notebook * Time Series Analysis (TSA) in Python - Linear Models to GARCH * Time Series and Sequential Data - Zoubin Ghahramani * A comprehensive beginner’s guide to create a Time Series Forecast (with Codes in Python) - Blog post * Simple Time Series Forecasting Models to Test So That You Don’t Fool Yourself - Blog post * How To Backtest Machine Learning Models for Time Series Forecasting - Blog post * Cross-validation for time series - Blog post * Time Series Analysis - Blog post * How to Make Baseline Predictions for Time Series Forecasting with Python - blog post * 7 Ways Time-Series Forecasting Differs from Machine Learning - blog post * Making Predictions with Sequences - blog post * 11 Classical Time Series Forecasting Methods in Python (Cheat Sheet) - blog post Category:Control Theory Category:Machine Learning Category:Probabilistic Graphical Models Category:Signal Processing